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HL: Halbleiterphysik

HL 15: Quanten-Hall-Effekt

HL 15.14: Vortrag

Dienstag, 27. März 2001, 13:45–14:00, S16

Statistics of Wavefunctions at the Quantum Hall Transition — •F. Evers¹, A. Mildenberger², and A.D. Mirlin^1,2 — ¹Institut für Nanotechnologie, Forschungszentrum Karlsruhe — ²Institut für Theorie der Kondensierten Materie, Universität Karlsruhe

Our current understanding of the plateau transition in the integer quantum Hall effect is based on the existence of a critical point at half filling. For a long time the corresponding critical field theory has not been known and it was only very recently that two conjectures have been made [1]. Both of them predict, that the distribution function P of −ln|ψ|², ψ denoting the quantum mechanical wave function, is strictly Gaussian. This is very remarkable, since 1) it is known that the generic behavior of P at a metal insulator transition in non-Gaussian, cf.[2], and 2) the published numerical data does not lend support to a Gaussian shape of P [3]. In order to resolve this striking discrepancy and decide whether or not the distribution function P is Gaussian we have performed very extensive numerical simulations the results of which will be presented in the talk.

[1] M.J.Bhaseen et. al., Nucl. Phys. B580 (2000) 688-720, M.R.Zirnbauer, hep-th/9905054. [2] A.D.Mirlin, F.Evers, Phys. Rev. B 61, 13774 (2000). [3] B.Huckestein, Rev. Mod. Phys. 67 (1995) 357.